Strong coupling between plasmons and excitons gives rise to new hybrid polariton states with potential applications in various fields. Despite a plethora of research on plasmon-exciton systems, their transient behaviour is not yet fully understood. Besides Rabi oscillations in the first few femtoseconds after optical excitation, coupled systems show interesting non-linear features on the picosecond time scale. Here, we conclusively show that the source of these features is heat that is generated inside the particles. Until now, this hypothesis was only based on phenomenological arguments. We investigate the role of heat by recording the transient spectra of plasmon-exciton core-shell nanoparticles with excitation off the polariton resonance. We present analytical simulations that precisely recreate the measurements solely by assuming an initial temperature rise of the electron gas inside the particles. The simulations combine established strategies for describing uncoupled plasmonic particles with a recently published model for static spectra. The simulations are consistent for various excitation powers, confirming that heating of the particles is indeed the root of the changes in the transient signals.